An amateur just solved a 60-year-old math problem\u2014by asking AI<\/p>\n
A ChatGPT AI has proved a conjecture with a method no human had thought of. Experts believe it may have further uses<\/p>\n
By Joseph Howlett<\/a> edited by Lee Billings<\/a><\/p>\n Eugene Mymrin\/Getty Images<\/p>\n Liam Price just cracked a 60-year-old problem that world-class mathematicians have tried and failed to solve. He\u2019s 23 years old and has no advanced mathematics training. What he does have is a ChatGPT Pro subscription, which gives him access to the latest large language models from OpenAI.<\/p>\n Artificial intelligence has recently made headlines<\/a> for solving a number of \u201cErdős problems,\u201d conjectures left behind by the prolific mathematician Paul Erdős. But experts have warned that these problems are an imperfect benchmark<\/a> of artificial intelligence\u2019s mathematical prowess. They range dramatically in both significance and difficulty, and many AI solutions have turned out to be less original than they appeared.<\/p>\n The new solution<\/a>\u2014which Price got in response to a single prompt to GPT-5.4 Pro and posted on www.erdosproblems.com<\/a>, a website devoted to the Erdős problems, just over a week ago\u2014is different. The problem it solves has eluded some prominent minds, bestowing it some esteem. And more importantly, the AI seems to have used a totally new method for problems of this kind. It\u2019s too soon to say with certainty, but this LLM-conceived connection may be useful for broader applications\u2014something hard to find among<\/a> recently touted AI triumphs in math.<\/p>\n On supporting science journalism<\/p>\n If you’re enjoying this article, consider supporting our award-winning journalism by subscribing<\/a>. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.<\/p>\n \u201cThis one is a bit different because people did look at it, and the humans that looked at it just collectively made a slight wrong turn at move one,\u201d says Terence Tao, a mathematician at the University of California, Los Angeles, who has become a prominent scorekeeper for AI\u2019s push into his field. \u201cWhat\u2019s beginning to emerge is that the problem was maybe easier than expected, and it was like there was some kind of mental block.\u201d<\/p>\n The question Price solved\u2014or prompted ChatGPT to solve\u2014concerns special sets of whole numbers, where no number in the set can be evenly divided by any other. Erdős<\/a> called these \u201cprimitive sets\u201d because of their connection to similarly indivisible prime numbers.<\/p>\n \u201cA number is prime if it has no other divisors, and this is kind of generalizing that definition from an individual number to a collection of numbers,\u201d says Jared Lichtman, a mathematician at Stanford University. Any set of prime numbers is automatically primitive, because primes have no factors (except themselves and the number one).<\/p>\n Erdős also came up with the Erdős sum, a \u201cscore\u201d you can calculate for any primitive set. He showed that the biggest the sum could be was about 1.6\u2014and conjectured that this value must also hold for the (infinite) set of all prime numbers. Lichtman proved Erdős right<\/a> as part of his doctoral thesis in 2022.<\/p>\n Erdős also noticed that the score drops if all of a set\u2019s numbers are large\u2014the larger the numbers, the lower the score. He guessed that the lowest this score could be was exactly one, a limit that the score would approach as the set\u2019s numbers approached infinity. Lichtman tried to prove this, too, but got stuck like everyone else before him.<\/p>\n Price wasn\u2019t aware of this history when he entered the problem into ChatGPT on an idle Monday afternoon. \u201cI didn\u2019t know what the problem was\u2014I was just doing Erdős problems as I do sometimes, giving them to the AI and seeing what it can come up with,\u201d he says. \u201cAnd it came up with what looked like a right solution.\u201d<\/p>\n He sent it to his occasional collaborator Kevin Barreto, a second-year undergraduate in mathematics at the University of Cambridge. The duo had jump-started the AI-for-Erdős craze late last year by prompting a free version of ChatGPT with open problems chosen at random from the Erdős problems website. (An AI researcher subsequently gifted them each a ChatGPT Pro subscription to encourage their \u201cvibe mathing.\u201d)<\/p>\n Reviewing Price\u2019s message, Barreto realized what they had was special, and experts whom he notified quickly took notice.<\/p>\n \u201cThere was kind of a standard sequence of moves that everyone who worked on the problem previously started by doing,\u201d Tao says. The LLM took an entirely different route, using a formula that was well known in related parts of math, but which no one had thought to apply to this type of question.<\/p>\n \u201cThe raw output of ChatGPT\u2019s proof was actually quite poor. So it required an expert to kind of sift through and actually understand what it was trying to say,\u201d Lichtman says. But now he and Tao have shortened the proof so that it better distills the LLM\u2019s key insight.<\/p>\n More importantly, they already see other potential applications of the AI\u2019s cognitive leap. \u201cWe have discovered a new way to think about large numbers and their anatomy,\u201d Tao says. \u201cIt\u2019s a nice achievement. I think the jury is still out on the long-term significance.\u201d<\/p>\n Lichtman is hopeful because ChatGPT\u2019s discovery validates a sense he\u2019s had since graduate school. \u201cI had the intuition that these problems were kind of clustered together and they had some kind of unifying feel to them,\u201d he says. \u201cAnd this new method is really confirming that intuition.\u201d<\/p>\n It\u2019s Time to Stand Up for Science<\/p>\n If you enjoyed this article, I\u2019d like to ask for your support. Scientific American has served as an advocate for science and industry for 180 years, and right now may be the most critical moment in that two-century history.<\/p>\n I\u2019ve been a Scientific American subscriber since I was 12 years old, and it helped shape the way I look at the world. SciAm always educates and delights me, and inspires a sense of awe for our vast, beautiful universe. I hope it does that for you, too.<\/p>\n If you subscribe to Scientific American<\/a>, you help ensure that our coverage is centered on meaningful research and discovery; that we have the resources to report on the decisions that threaten labs across the U.S.; and that we support both budding and working scientists at a time when the value of science itself too often goes unrecognized.<\/p>\n In return, you get essential news, captivating podcasts<\/a>, brilliant infographics, can’t-miss newsletters<\/a>, must-watch videos, challenging games<\/a>, and the science world’s best writing and reporting. 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I hope you\u2019ll support us in that mission.<\/p>\n","protected":false},"excerpt":{"rendered":"April 24, 2026 4 min read Add Us On GoogleAdd SciAm An amateur just solved a 60-year-old math…\n","protected":false},"author":2,"featured_media":605114,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[45],"tags":[182,181,507,74],"class_list":{"0":"post-605113","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-artificial-intelligence","8":"tag-ai","9":"tag-artificial-intelligence","10":"tag-artificialintelligence","11":"tag-technology"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/605113","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/comments?post=605113"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/posts\/605113\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media\/605114"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/media?parent=605113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/categories?post=605113"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/us\/wp-json\/wp\/v2\/tags?post=605113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"An](\"https:\/\/www.newsbeep.com\/us\/wp-content\/uploads\/2026\/04\/abstract-rubiks-cube.jpg\")
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